Volkswagen's five senior board members are meeting to discuss the company's fate after it was caught manipulating US diesel car emissions tests.
The revelation has sparked a wide number of investigations and could result in huge financial damage.
There is speculation over the position of VW chief Martin Winterkorn. His contract is up for renewal on Friday.
Meanwhile Germany has said it is considering launching a criminal inquiry into the scandal.
"In connection with the allegations of emission gas manipulation in VW diesel engines, the public prosecutors of Brunswick are considering launching a probe against management employees at Volkswagen," the prosecutors said in a statement.
Volkswagen, the world's biggest carmaker, has admitted it deceived US regulators in exhaust emissions tests by installing a device to give more positive results.
Reports in Germany suggest VW boss Mr Winterkorn has lost the support of key investors as a result.
Analyst Arndt Ellinghorst at Evercore ISI said: "VW needs a fresh start and in our view a new CEO."
The whole Volkswagen board will hold a scheduled meeting on Friday, although an announcement may come ahead of that.
Volkswagen has said 11 million vehicles worldwide are involved and it is setting aside €6.5bn (£4.7bn) to cover costs of the scandal.
VW shares fell by about 30% on Monday and Tuesday but recovered some ground on Wednesday.
Analysis: Theo Leggett, business reporter, Wolfsburg
Wolfsburg is Volkswagen Town. It was founded in the 1930s to house workers building the KdF Wagen - the machine that became the Volkswagen Beetle.
Like Detroit in the US, it owes its fortunes largely to the car industry - but unlike Detroit, it is still a wealthy and prosperous place. It is dominated by the firm's 6.5km2 factory - and the VW badge is everywhere.
That is why the scandal at VW really matters to people here. 72,000 people work in the factory - more than half of the town's population.
Most of the rest work in service industries which depend on VW employees for their business - shops, restaurants and the like. Even the tourist industry is largely focused on the Autostadt - a giant car-based theme park. If VW falls on hard times, so, very probably, will Wolfsburg
The effects will also be felt more widely. The company is a major contributor to the economy of the state of Lower Saxony as a whole. Indeed, the regional government has a 20% stake in the business. And for Germany itself, it is a national champion, a symbol of German manufacturing pride.
So the Volkswagen scandal could threaten the entire social fabric of Wolfsburg, seriously hurt the economy of Lower Saxony and deliver a sizeable wound to German national pride. As the company's directors look for ways to limit the fallout and rebuild trust in the brand, there really is a great deal at stake.
In the US, the Environmental Protection Agency and the California Air Resources Board are investigating the way VW cheated tests to measure the amount of pollutants coming from its diesel cars.
According to news agencies Bloomberg and AFP, the Department of Justice is also looking into the issue, which raises the possibility of the company and individual executives facing criminal charges.
A DoJ criminal investigation would be serious, as federal authorities can bring charges with severe penalties against a firm and individuals.
Late on Tuesday, New York state's top lawyer also announced an investigation.
On Tuesday, Mr Winterkorn issued a fresh apology for the test-rigging, saying he was "endlessly sorry" for the "manipulation".
The boss of Volkswagen's US business, Michael Horn, has also admitted the firm "totally screwed up".
In the UK, the Department of Transport has added its voice to calls for an EU-wide investigation into the affair.
News of the fake tests emerged last Friday, when the US Environmental Protection Agency (EPA) said VW diesel cars had much higher emissions than tests had suggested and that software in several diesel cars could deceive regulators.
As a result Volkswagen was ordered to recall half a million cars in the US.
The EPA found the "defeat device", the device that allowed VW cars to emit less during tests than they would while driving normally, in diesel cars including the Audi A3 and the VW Jetta, Beetle, Golf and Passat models.
VW has stopped selling the relevant diesel models in the US, where diesel cars account for about a quarter of its sales.
The EPA said that the fine for each vehicle would be up to $37,500 (£24,000). With 482,000 cars sold since 2008 involved in the allegations, it means the fines could reach $18bn.
That would be a considerable amount, even for the company that recently overtook Toyota to be the world's top-selling vehicle maker in the first six months of the year.
Industry experts are concerned about what this means more widely for diesel car manufacturers.
Jim Holder, editorial director of Haymarket Automotive, whose titles include WhatCar and AutoCar, told the BBC that there had never been a scandal in the industry of this size, and that it could make diesel engines for cars uneconomical.
However, Martin Leach, a consultant at Magma and a former head of Ford Europe, told the BBC that the problem is unlikely to emerge elsewhere.
"I don't think it will extend to other manufacturers. Volkswagen has really engaged to try to beat standards in the US. I would be surprised if it spreads outside the US as Europe's testing standards were more advanced and therefore more difficult to cheat than the US."